Segmentation-free Quantification of Spots on a Homogeneous Background

A recurrent problem in biological image analysis is to quantify the number and size of spots on a homogeneous background. Most automated approaches rely on segmenting the individual spots, which becomes unreliable when the image contains artifacts, noise, or confounding objects. Therefore, practitioners often resort to tedious and time-consuming manual counting and measurements. As an alternative, we propose a visual analytics approach to this problem. It is based on Total Variation Flow, a partial differential equation that changes the intensities of image regions at a rate inverse to their scale. From this, we derive novel quantitative per-pixel measures of scale and density, and we show how the results can be combined with tools for visualization and selection to achieve a fast summary of median size and spot density in an image. Given a set of images, our framework places them on a 2D map that makes it easy to quickly compare them with respect to spot sizes and density. Our system is applied to real-world data from Stimulated Emission Depletion (STED) microscopy.